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On level and collision sets of some Feller processes
- Publication Year :
- 2014
-
Abstract
- This paper is about lower and upper bounds for the Hausdorff dimension of the level and collision sets of a class of Feller processes. Our approach is motivated by analogous results for L\'evy processes by Hawkes (for level sets), Taylor and Jain & Pruitt (for collision sets). Since Feller processes lack independent or stationary increments, the methods developed for L\'evy processes cannot be used in a straightforward manner. Under the assumption that the Feller process possesses a transition probability density, which admits lower and upper bounds of a certain type, we derive sufficient conditions for regularity and non-polarity of points; together with suitable time changes this allows us to get upper and lower bounds for the Hausdorff dimension.
- Subjects :
- Mathematics - Probability
Primary 60G17, Secondary: 60J75, 60J25, 28A78, 35S05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1412.8726
- Document Type :
- Working Paper